The D-Boussinesq equation: Hamiltonian and symplectic structures; Noether and inverse Noether operators

Abstract

Using new methods of analysis of integrable systems,based on a general geometric approach to nonlinear PDE,we discuss the Dispersionless Boussinesq Equation, which is equivalent to the Benney-Lax equation,being a system of equations of hydrodynamical type. The results include: a description of local and nonlocal Hamiltonian and symplectic structures, hierarchies of symmetries, hierarchies of conservation laws, recursion operators for symmetries and generating functions of conservation laws. Highly interesting are the appearences of the Noether and Inverse Noether operators ,leading to multiple infinite hierarchies of these operators as well as recursion operators